Yes, creatures in the Antimagic field take turns as normal.
Time stops for everyone except the caster & those in the Antimagic Field.
TimestopTime Stop is a spell, the described occurance “Time stops for everyone” is a discrete magical effect. Since Antimagic Field suppresses magical effects, Timestop does not function in the Antimagic sphere.
Magical effects are suppressed in the Antimagic sphere and can’t protrude into it. PHB 213
What is a Spell? A spell is a discrete magical effect, a single shaping of the magical energies that suffuse the multiverse into a specific, limited expression. PHB 201
While an effect is suppressed, it doesn’t function, but the time it spends suppressed counts against it’s duration.
If the sphere overlaps an area of magic, the part of the area that is covered by the sphere is suppressed.
Any active spell or other magical effect on a creature in the sphere is suppressed while the creature is in it.